My loom has a serial number but I think it's a fairly early model and doesn't seem to indicate the year. From the style of decal I've decided it is probably from somewhere around 1945-1955. Why? Because by 1956 they were including the year. Since mine doesn't have a year, I think it must pre-date 1956.
The number isn't easy to see. I finally found it to the left of the treadles on the cross piece that holds the treadles. A light aimed sideways on revealed the date. The imprint says F-36-11215.